MRI TV-Rician Denoising

Abstract

Recent research on magnitude Magnetic Resonance Images (MRI) reconstruction from the Fourier inverse transform of complex (gaussian contaminated) data sets focuses on the proper modeling of the resulting Rician noise contaminated data. In this paper we consider a variational Rician denoising model for MRI data sets that we solve by a semi-implicit numerical scheme, which leads to the resolution of a sequence of Rudin, Osher and temi (ROF) models. The (iterated) resolution of these well posed numerical problems is then proposed for Total Variation (TV) Rician denoising. For numerical comparison we also consider a direct semi-implicit approach for the primal problem which amounts to consider some (regularizing) approximating problems. Synthetic and real MR brain images are then denoised and the results show the effectiveness of the new method in both, the accuracy and the speeding up of the algorithm. © Springer-Verlag Berlin Heidelberg 2013.